1. Field of the Invention
The present invention relates to the field of translinear circuits, including current multipliers, bandgap reference circuits, and proportional-to-absolute-temperature sensor circuits. Specifically, the present invention relates to compensation for extrinsic series base and emitter resistance inherent in bipolar transistors within the translinear circuits.
2. Discussion of the Related Art
Proportional-to-absolute-temperature (PTAT) temperature sensors and bandgap reference circuits determine their output values based upon the difference in the voltage drops on diode junctions having different current densities. The primary property exploited by these circuits is the exponential variation of the current density across a p-n junction barrier with the intrinsic voltage applied on that barrier. A larger class of such circuits are the translinear (TL) networks. All the translinear circuits are based on the logarithmic variation of the intrinsic base-emitter voltage of a bipolar transistor with its collector current. There are several sources of errors which limit the accuracy of these translinear circuits. The V.sub.BE mismatches in nominal identical pairs due to emitter area differences, process gradients, and mechanical stress, can be minimized by interdigitation and common centroid layouts. The influence of base width modulation by the base-collector voltage (the Early effect) on the collector current can also be minimized by cascode configurations or active biasing for constant V.sub.CB. Usually, larger errors are due to the finite current gain .beta. and finite base current. These errors are usually minimized by using driver stages or base current cancellation techniques.
Often the limiting factor in the accuracy of translinear circuits comes from the extrinsic base resistance and the series emitter resistance. While their effect is negligible at very low current densities, such as in micropower applications, the errors introduced at even moderate current densities usually dominate the non-idealities in the system. Attempts to compensate the base resistance with other resistors have only a limited success due to the poor matching between the base resistance and the compensation resistor, which also have different temperature coefficients.
A classic example of a translinear circuit is the Brokaw bandgap circuit, shown in FIG. 1. The two bipolar transistors Q.sub.1 and Q.sub.2 have different emitter areas. Specifically, transistor Q.sub.2 is K times larger in emitter area than transistor Q.sub.1. The feedback loop including the operational amplifier A.sub.1 ensures that the same current I flows through both transistors Q.sub.1 and Q.sub.2.
Because transistor Q2 is larger in area than transistor Q1, the current densities in the junctions of transistor Q2 are less by a factor of K than the corresponding densities in transistor Q1 when the same total collector current I flows through both transistors. Thus, the voltage drop across the base to emitter p-n junction of transistor Q2 is smaller than the corresponding voltage drop for transistor Q1. The difference in the base-emitter voltage of the two transistors .DELTA.V.sub.be occurs across the resistor R.sub.1. The equilibrium value for the bias current I is given by ##EQU1##
where ##EQU2##
and kT/q represents the thermal voltage, which is proportional to absolute temperature T measured in Kelvin degrees. Since Q1 and Q2 have emitter areas ratioed by a factor of K, I.sub.sat2 =K*I.sub.sat1, and eq. (2) reduces to the following ##EQU3##
The output voltage V.sub.BG in FIG. 1, can be expressed as follows. ##EQU4##
For a certain ratio of the resistors R.sub.1 and R.sub.2, V.sub.BG becomes equal to the bandgap voltage, and it is essentially temperature independent. Importantly, the cancellation of the output voltage temperature dependence is obtained independently of the absolute value of the resistors R.sub.1 and R.sub.2, which is difficult to control.
Eq. (2) assumes an ideal behavior for the bipolar transistor and neglects the voltage drops on the emitter and base extrinsic series resistors. The extrinsic base-emitter voltage of a transistor can be expressed as follows. ##EQU5##
In the above equation, R.sub.e -is the emitter series resistance, R.sub.b -is the base series resistance , .beta.-is the dc current gain, and I/(.beta.+1) is the base current.
For many applications, such as temperature sensors and low-noise bandgap references, the current densities are large enough so the series resistance voltage drops (the last two terms in eq. (5)) become significant. The equilibrium bias current in this case can be calculated from ##EQU6##
In eq. (6), it is assumed that the series resistances R.sub.b and R.sub.c are inversely proportional to the emitter area, such that ##EQU7##
In practice, the resistor R.sub.1 is technologically different from internal resistors R.sub.b and R.sub.e, and they have different temperature coefficients. In particular, it is very hard to control the ratio of these internal resistances to the other resistors in the circuit R.sub.1 and R.sub.2. For a PTAT current source, even though R.sub.1 can be made with a zero temperature coefficient (zero TC), the errors due to the extra terms in eq. (6) introduce errors in the ideal PTAT variation. In particular, the .DELTA.V.sub.be voltage drop variation between the two junctions with different current densities is not PTAT any longer, but includes a term dependent on the ratio of resistors R.sub.b, R.sub.e and R.sub.1. ##EQU8##
Conventional ways to circumvent this problem in PTAT temperature sensors have been proposed by using three different current densities and then to compensate for the IR drops using complicated computations, which are inherently undesirable due to their significant complexity.